scholarly journals Numerical Simulation of Unsteady-State Flow in Dual Porous Coalbed Methane Horizontal Wells with Complex Boundary Conditions

2015 ◽  
Vol 2015 ◽  
pp. 1-11
Author(s):  
Cheng-yong Li ◽  
Jun Zhou ◽  
Xiang-yi Yi ◽  
Yi Luo ◽  
Ping-zhi Gong
Keyword(s):  
Boundary Conditions ◽  
Coalbed Methane ◽  
Gas Flow ◽  
Flow Characteristics ◽  
Horizontal Wells ◽  
Basic Solution ◽  
Pressure Derivative ◽  
Type Curves ◽  
Complex Boundary ◽  
Lord Kelvin

The bottom-hole pressure response which can reflect the gas flow characteristics is important to study. A mathematical model for description of gas from porous coalbed methane (CBM) reservoirs with complex boundary conditions flowing into horizontal wells has been developed. Meanwhile, basic solution of boundary elements has been acquired by combination of Lord Kelvin point source solution, the integral of Bessel function, and Poisson superimpose formula for CBM horizontal wells with complex boundary conditions. Using this model, type curves of dimensionless pressure and pressure derivative are obtained, and flow characteristics of horizontal wells in complex boundary reservoirs and relevant factors are accordingly analyzed.

Pressure-Transient Behavior of Multisegment Horizontal Wells With Nonuniform Production: Theory and Case Study

2018 ◽  
Vol 140 (9) ◽  
Author(s):  
Youwei He ◽  
Shiqing Cheng ◽  
Jiazheng Qin ◽  
Yang Wang ◽  
Zhiming Chen ◽  
...  
Keyword(s):  
Horizontal Wells ◽  
Transient Behavior ◽  
Field Application ◽  
Pressure Derivative ◽  
Pressure Transient ◽  
Type Curves ◽  
Horizontal Wellbore ◽  
Estimate Rate ◽  
Calculated Average

Field data indicate production profile along horizontal wells is nonuniform. This paper develops an analytical model of multisegment horizontal wells (MSHWs) to estimate rate distribution along horizontal wellbore, interpret the effective producing length (EPL), and identify underperforming horizontal sections using bottom-hole pressure (BHP) data. Pressure solutions enable to model an MSHW with nonuniform distribution of length, spacing, rate, and skin factor. The solution is verified with the analytical solution in commercial software. Type curves are generated to analyze the pressure-transient behavior. The second radial-flow (SRF) occurs for the MSHWs, and the duration of SRF depends on interference between segments. The pressure-derivative curve during SRF equals to 0.5/Np (Np denotes the number of mainly producing segments (PS)) under weak interference between segments. The calculated average permeability may be Np times lower than accurate value when the SRF is misinterpreted as pseudoradial-flow regime. The point (0, 0, h/2) are selected as the reference point, and symmetrical cases will generate different results, enabling us to distinguish them. Finally, field application indicates the potential practical application to identify the underperforming horizontal segments.

scholarly journals Solution and type curves for the seepage model of the water-bearing coalbed with leakage recharge

2017 ◽  
Vol 21 (1) ◽  
pp. 17 ◽  
Author(s):  
Wangang Chen ◽  
Yu Yang ◽  
Hansen Sun ◽  
Chengwei Zhang ◽  
Qin Wen ◽  
...  
Keyword(s):  
Coalbed Methane ◽  
Radial Flow ◽  
Curve Matching ◽  
Pressure Derivative ◽  
Type Curve ◽  
Type Curves ◽  
Reservoir Permeability ◽  
Leakage Coefficient ◽  
Seepage Theory ◽  
Seepage Model

To analyze the effects of the leakage recharge of the aquifer on the initial dewatering of coalbed methane wells, the mathematical seepage model of water in the coalbed considering the aquifer leakage was established by using the leakage coefficient according to the unsteady seepage theory. The model was solved after Laplace transform and the Stehfest numerical reverse inversion was used to obtain the solution in right space. Then, the log-log type curves of pressure and pressure derivative were created with new combinations of parameters. Based on the natural seepage mechanism, the influence of aquifer leakage on curve shape was judged. It is found that the radial flow ends earlier as the leakage coefficient increases. Moreover, it was proposed to obtain reservoir permeability, skin factor, and leakage coefficient by using type curve matching. The type curves are useful for quantitatively evaluating the level of leakage, thereby guiding the adjustment of the following production system for CBM wells. Curvas de solución y tipo para el modelo de filtración de capas carboníferas acuíferas con recarga de fugasResumenEste estudio estableció el modelo matemático de filtración de agua en una capa carbonífera al estimar la salida acuífera con el uso del coeficiente de fuga, de acuerdo con la teoría de filtración inestable, para analizar los efectos en la recarga de pérdida de fluidos de un acuífero en el drenado inicial para pozos de gas metano.  El modelo se resolvió tras usar la transformación Laplace y la inversión numérica Stehfest para encontrar la respuesta en el lugar indicado. Luego, se creó la representación algorítmica de la presión y la presión derivativa con nuevas combinaciones de parámetros. Se evaluó la influencia de la pérdida de fluido del acuífero en la forma de la curva con base al mecanismo físico de filtración. Se estableció que el flujo radial finaliza antes de que el coeficiente de pérdida de fluido se incremente. Además, se propone el uso de la curva tipo correspondiente para obtener la permeabilidad del reservorio, el factor de daño y el coeficiente de pérdida de fluido. Las curvas tipo son útiles para evaluar cuantitativamente el nivel de la pérdida de fluido, y de esta manera guiar el ajuste de un sistema de producción consecuente para pozos de gas metano de carbón.

scholarly journals A Semianalytical Solution for Multifractured Horizontal Wells in Box-Shaped Reservoirs

2014 ◽  
Vol 2014 ◽  
pp. 1-12 ◽  
Author(s):  
Lei Wang ◽  
Xiaodong Wang ◽  
He Zhang ◽  
Yunpeng Hu ◽  
Chen Li
Keyword(s):  
Radial Flow ◽  
Flow Characteristics ◽  
Horizontal Wells ◽  
Flow Region ◽  
Linear Flow ◽  
Type Curves ◽  
Production Ratio ◽  
Dirac Function ◽  
Sensitive Parameters ◽  
First Time

This paper presented a 3D point sink model through using Dirac function. Then, 3D point sink solution in boxed reservoirs was obtained through using Laplace transform and Fourier transform methods. Based on the flux and pressure equivalent conditions in Laplace space, a semianalytical solution for multifractured horizontal wells was also proposed for the first time. The production rate distribution was discussed in detail for multifractured horizontal wells. The calculative results show the outermost fractures had higher production ratio due to larger drainage area and the inner fractures were lower due to the strong interface between fractures. Type curves were established to analyze the flow characteristics, which would be divided into six stages, for example, bilinear flow region, the first linear flow region, the first radial flow region, the second linear flow region, the second radial flow region, and the boundary dominated flow region, respectively. Finally, effects of some sensitive parameters on type curves were also analyzed in detail.

scholarly journals Method for Calculating Transients in a Gas Pipeline

2021 ◽  
Vol 64 (5) ◽  
pp. 426-458
Author(s):  
A. S. Fikov
Keyword(s):  
Boundary Conditions ◽  
Analytical Model ◽  
Flow Rate ◽  
Gas Flow ◽  
Initial Moment ◽  
Gas Pipelines ◽  
Gas Flow Rate ◽  
Labor Costs ◽  
Duhamel Integral ◽  
Complex Boundary

Abstaract. An analytical solution of a system of partial differential equations describing the unsteady isothermal flow of real gases in gas pipelines is considered. Such a problem arises when studying the regularity of alterations in the instantaneous values of pressure and gas flow in main gas pipelines, for example, during startups and shutdowns of large gas consumers. Meanwhile, transients are not necessarily of a pronounced oscillatory nature, despite the fact that they are described by periodic functions. In the course of the research, the task was set to obtain a mathematical model of the process taking into account the inertial term of the equation of motion, the neglect of which is possible only if the friction losses are exceeded by 3.5–4 times over the shock pressure. An important feature of the solution that have been found is its universality, which makes it possible to significantly reduce labor costs when using it to find partial solutions to practical problems that differ in boundary conditions. The boundary conditions of the first kind are given as an arbitrary function of both the gas flow rate and its pressure. The solution is based on the widely used method of separation of Fourier variables. In order to simplify the calculations, the original differential equation is transformed in such a way that the boundary conditions acquire the property of homogeneity. It has been determined that the requirements that the boundary conditions are equal to zero at the initial moment of time introduced into the solution make it possible to obtain a concise record of the obtained analytical model, but do not limit the area of the use of the model with a surge change in the gas flow rate or pressure. The obtained analytical model of unsteady gas flow makes it possible, without using the Duhamel integral, to find analytical solutions under more complex boundary conditions than the flow rate jump. At the same time, the solutions found completely coincide with the solutions based on the Duhamel integral, but in the course of the solution that we have found it is possible to avoid integration, which has a positive effect on the applicability of this approach in the practice of engineering calculations.

scholarly journals One-Dimensional Numerical Analysis of Cross-Sectional Area Variation Effects on Flow through the Gas Turbine Diffuser

2019 ◽  
Author(s):  
Nima Zamani Meymian ◽  
Reza Khodadadi
Keyword(s):  
Mach Number ◽  
Boundary Conditions ◽  
Gas Turbine ◽  
Cross Section ◽  
Gas Flow ◽  
Flow Characteristics ◽  
Time Step ◽  
Cross Sectional ◽  
One Dimensional ◽  
Length Changes

In the paper, a one-dimensional compressible flow of gas inside the gas turbine’s diffuser has been simulated. The modeling has been performed to the aim of obtaining boundary conditions of outlet gas from diffuser and inlet gas to the combustion chamber. Depending on working flow regimes of fluid including subsonic, transonic, and supersonic flows, changes of diffuser cross-section have different effects on gas flow characteristics. For these effects to be correctly imposed, Mach number of the gas flow in each time-step affected by changes of cross-section would be determined, depending on the local Mach number in the same time-step. Obtaining distribution of Mach number along diffuser length, changes in other main characteristics of flow such as pressure, temperature, speed, and density for all of the points along diffuser length would be obtained. In order to verify the validity of the numerical algorithm used, the gas flow would be solved in a divergent nozzle and compared to other numerical methods. In the end, using gas turbine diffuser’s geometrical information, compressible gas flow inside it would be studied using the actual boundary conditions for a 25 MW gas turbine.

Sign in / Sign up

Export Citation Format

Share Document